2(3x+1)2x=18

Solution for 2(3x+1)2x=18 equation:

2(3x+1)2x=18

We move all terms to the left:

2(3x+1)2x-(18)=0

We multiply parentheses

12x^2+4x-18=0

a = 12; b = 4; c = -18;
Δ = b2-4ac
Δ = 42-4·12·(-18)
Δ = 880
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{880}=\sqrt{16*55}=\sqrt{16}*\sqrt{55}=4\sqrt{55}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(4)-4\sqrt{55}}{2*12}=\frac{-4-4\sqrt{55}}{24}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(4)+4\sqrt{55}}{2*12}=\frac{-4+4\sqrt{55}}{24}
$